Find the theoretically optimal fraction of capital to risk per trade, based on your win rate and payoff ratio.
Kelly % = W − (1−W)/R, where W is win probability (as a decimal) and R is the ratio of average win to average loss. Most practitioners use a fraction (e.g. half-Kelly) rather than the full amount, since full Kelly can be aggressive.
Educational tool only — not investment advice. Markets involve risk; past performance and illustrative math don't guarantee future results.
The Kelly Criterion, developed by John Kelly at Bell Labs in 1956 and later famously applied by mathematician Ed Thorp (first to beat casino blackjack, later to run a successful hedge fund), calculates the mathematically optimal fraction of capital to risk on a bet or trade to maximize long-term compound growth. The formula — f* = (bp − q) / b, where p is the probability of winning, q is the probability of losing (1 − p), and b is the ratio of average win size to average loss size — identifies a specific sweet spot: betting less than this fraction grows wealth more slowly than necessary, while betting more than it actually produces lower long-run growth and real risk of ruin, even though it might feel more aggressive and potentially more rewarding in the short run.
The practical catch is that full Kelly sizing is genuinely aggressive in real-world use — in many trading and betting scenarios the raw formula suggests risking 15-20% or more of capital on a single position, and that number is only as good as the win-probability and payoff-ratio inputs feeding it, which are themselves estimates, not certainties. Overconfident inputs (assuming a better edge than actually exists) produce a Kelly-sized bet that's too aggressive for the real, messier edge, leading to painful drawdowns when reality falls short of the estimate. This is exactly why most practitioners use fractional Kelly — commonly half-Kelly or quarter-Kelly — deliberately betting a fraction of what the formula suggests, trading away some theoretical growth rate for meaningfully smoother, less punishing drawdowns.
It calculates the fraction of capital that, when bet or invested repeatedly, mathematically maximizes long-term compound growth rate — not the fraction that maximizes a single bet's expected value, which is a subtly different (and more dangerous) goal. The formula is f* = (bp − q) / b, using win probability, loss probability, and the win/loss payoff ratio.
Because betting beyond the Kelly-optimal fraction increases volatility and drawdown risk faster than it increases long-run growth, and taken far enough, overbetting leads to a real risk of ruin — losing so much capital that recovery becomes mathematically very difficult. The Kelly fraction is specifically the point that maximizes growth; going past it makes growth worse, not better.
Because full Kelly sizing is genuinely aggressive — often suggesting 15-20%+ of capital on a single position — and the formula's output is only as reliable as its win-probability and payoff-ratio inputs, which are estimates. Half-Kelly or quarter-Kelly sizing trades away some theoretical growth rate for meaningfully smoother returns and smaller drawdowns when those estimates turn out to be optimistic.
The formula will recommend a position size larger than what your actual (lower) edge justifies, since Kelly sizing is highly sensitive to its input assumptions. This is one of the most common real-world failure modes of Kelly sizing — the math is correct, but garbage-in-garbage-out applies directly to how aggressive the suggested bet size becomes.